QUANTIZATION OF MONOPOLES WITH NON-ABELIAN MAGNETIC CHARGE

Magnetic monopoles in Yang-Mills-Higgs theory with a non-abelian unbro ken gauge group are classified by holomorphic charges in addition to t he topological charges familiar from the abelian case. As a result the moduli spaces of monopoles of given topological charge are stratified according to the holomorphic charges. Here the physical consequences of the stratification are explored in the case where the gauge group S U(3) is broken to U(2). The description due to Dancer of the moduli sp ace of charge-two monopoles is reviewed and interpreted physically in terms of non-abelian magnetic dipole moments. Semi-classical quantisat ion leads to dyonic states which are labelled by a magnetic charge and a representation of the subgroup of U(2) which leaves the magnetic ch arge invariant (centraliser subgroup). A key result of this paper is t hat these states fall into representations of the semi-direct product U(2) times sign with bar connected to left of it R-4, The combination rules (Clebsch-Gordan coefficients) of dyonic states can thus be deduc ed. Electric-magnetic duality properties of the theory are discussed i n the light of our results, and supersymmetric dyonic BPS states which fill the SL(2,Z) orbit of the basic massive W-bosons are found. (C) 1 998 Elsevier Science B.V.